Neutron Transfer Reactions for Deformed Nuclei Using Sturmian Basis States

Abstract. We study the spin-parity distribution P(Jπ,E) of 156Gd excited states above the neutron separation energy Sn = 8.536 MeV [1] that are expected to be populated via the 1-step neutron pickup reaction 157Gd(3He,4He)156Gd. In analogy with the rotor plus particle model [2], we view excited states in 156Gd as rotational excitations built on intrinsic states consisting of a neutron hole in the 157Gd core; that is, a neutron removal from a deformed Woods-Saxon type single-particle state [3] in 157Gd. The particle-core interaction usually dominated by a Coriolis coupling are accounted via first order perturbation theory [4]. The reaction cross section to each excited state in 156Gd is calculated as coherent contribution using a standard reaction code [5] based on spherical basis states. The spectroscopic factor associated with each state is the expansion coefficient of the deformed neutron state in a spherical Sturmian basis along with the spherical form factors [4]. The total cross section, as a function of the excitation energy, is generated using Lorentzian smearing distribution function. Our calculations show that, within the assumptions and computational modeling, the reaction 3He + 157Gd → 4He + 156Gd&ast; has a smooth formation probability P(Jπ,E) within the energy range relevant to the desired reaction 155Gd + n → 156Gd&ast;. The formation probability P(Jπ,E) resembles a Gaussian distribution with centroids and widths that differ for positive and negative parity states.